{"abstract":[{"text":"We consider a model of the Riemann zeta function on the critical axis and study its maximum over intervals of length (log T)θ, where θ is either fixed or tends to zero at a suitable rate.\r\nIt is shown that the deterministic level of the maximum interpolates smoothly between the ones\r\nof log-correlated variables and of i.i.d. random variables, exhibiting a smooth transition ‘from\r\n3/4 to 1/4’ in the second order. This provides a natural context where extreme value statistics of\r\nlog-correlated variables with time-dependent variance and rate occur. A key ingredient of the\r\nproof is a precise upper tail tightness estimate for the maximum of the model on intervals of\r\nsize one, that includes a Gaussian correction. This correction is expected to be present for the\r\nRiemann zeta function and pertains to the question of the correct order of the maximum of\r\nthe zeta function in large intervals.","lang":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2103.04817"}],"department":[{"_id":"LaEr"}],"language":[{"iso":"eng"}],"article_number":"2103.04817","_id":"9230","ec_funded":1,"date_published":"2021-03-08T00:00:00Z","citation":{"mla":"Arguin, Louis-Pierre, et al. “Maxima of a Random Model of the Riemann Zeta Function over Intervals of Varying Length.” <i>ArXiv</i>, 2103.04817, doi:<a href=\"https://doi.org/10.48550/arXiv.2103.04817\">10.48550/arXiv.2103.04817</a>.","ieee":"L.-P. Arguin, G. Dubach, and L. Hartung, “Maxima of a random model of the Riemann zeta function over intervals of varying length,” <i>arXiv</i>. .","apa":"Arguin, L.-P., Dubach, G., &#38; Hartung, L. (n.d.). Maxima of a random model of the Riemann zeta function over intervals of varying length. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2103.04817\">https://doi.org/10.48550/arXiv.2103.04817</a>","ista":"Arguin L-P, Dubach G, Hartung L. Maxima of a random model of the Riemann zeta function over intervals of varying length. arXiv, 2103.04817.","chicago":"Arguin, Louis-Pierre, Guillaume Dubach, and Lisa Hartung. “Maxima of a Random Model of the Riemann Zeta Function over Intervals of Varying Length.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2103.04817\">https://doi.org/10.48550/arXiv.2103.04817</a>.","ama":"Arguin L-P, Dubach G, Hartung L. Maxima of a random model of the Riemann zeta function over intervals of varying length. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2103.04817\">10.48550/arXiv.2103.04817</a>","short":"L.-P. Arguin, G. Dubach, L. Hartung, ArXiv (n.d.)."},"publication_status":"submitted","date_updated":"2023-05-03T10:22:59Z","external_id":{"arxiv":["2103.04817"]},"month":"03","article_processing_charge":"No","doi":"10.48550/arXiv.2103.04817","day":"08","publication":"arXiv","author":[{"full_name":"Arguin, Louis-Pierre","last_name":"Arguin","first_name":"Louis-Pierre"},{"id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","full_name":"Dubach, Guillaume","first_name":"Guillaume","last_name":"Dubach","orcid":"0000-0001-6892-8137"},{"first_name":"Lisa","last_name":"Hartung","full_name":"Hartung, Lisa"}],"type":"preprint","project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"status":"public","acknowledgement":"The research of L.-P. A. is supported in part by the grant NSF CAREER DMS-1653602. G. D. gratefully acknowledges support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. The research of L. H. is supported in part by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through Project-ID 233630050 -TRR 146, Project-ID 443891315 within SPP 2265 and Project-ID 446173099.","title":"Maxima of a random model of the Riemann zeta function over intervals of varying length","year":"2021","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2021-03-09T11:08:15Z","oa":1,"oa_version":"Preprint"}